One formula instead of four cases
Show that for every . Why does the phase shift remove the need to treat separately?
Open in channelRida Abu-Sokon · RIDA MATH
Learn deeply.Solve clearly.
The mathematics practice of Rida Abu-Sokon, a teacher and independent Jordanian researcher in integral transforms and differential operators. Private university tutoring, consultation, structured learning, a moderated community, and an interactive Math Lab — built on one conviction: complex mathematics becomes clearer when its structure is revealed.
For studentsPrivate tutoring & problem-solving For researchers & engineersConsultation & research discussion
Or start exploring: Math Lab · Learning pathways · The book
- Calculus I–III
- Differential equations
- Linear algebra
- Integral transforms
- Complex variables
- Matrix methods
Start where you are
Five ways in, each with a clear next step.
RIDA MATH serves people with different needs. Choose the description closest to yours.
- 01
University student
A course, an exam, or a concept that will not settle.
- 02
Advanced or graduate learner
Transforms, ODEs, complex variables, or reading research.
- 03
Researcher or engineer
A model, a derivation, or a method choice to think through.
- 04
Educator or institution
A lecture, a workshop series, or learning material.
- 05
Independent explorer
Ideas to read, instruments to try, people to think with.
Areas of expertise
University mathematics, with depth in analysis, transforms, and matrices.
Rida's research interests — integral transforms, differential operators, higher-order derivatives, and matrix-based techniques — shape how every subject is taught: through its structure.
- 01
Calculus and analysis
Limits, differentiation, integration, series, and parameter-dependent integrals — including the higher-order derivative methods developed in Rida's book.
Calculus I–III · Multivariable calculus · Series · Differentiation under the integral sign
- 02
Differential equations
First-order and linear constant-coefficient ODEs, initial value problems, systems, and transform-based solution methods.
First-order ODEs · Linear ODEs · Initial value problems · Laplace methods
- 03
Integral transforms
Laplace, Fourier, and Mellin transforms read through kernels, convergence, and operator structure — the core of Rida's research interests.
Laplace · Fourier · Mellin · Convolution
- 04
Linear algebra and matrix methods
Vector spaces, bases, linear maps, and the matrix representation of differentiation used in the Matrix Boundary Method.
Vector spaces · Matrices · Eigenstructure · Differentiation matrices
- 05
Complex numbers and root structure
Polar form, complex roots, rational functions, and the geometric reading of derivatives through root positions.
Polar form · Complex roots · Rational functions · Root geometry
- 06
Reading and discussing research mathematics
Unpacking notation, definitions, and claims in technical material, and discussing analytical ideas with precision.
Technical reading · Notation · Argument structure · Mathematical writing
Private tutoring and student support
One-to-one sessions that make the method yours.
Sessions follow your own course. A short diagnostic finds the real gap; a written plan orders the topics; each session ends with a summary and practice matched to what was found.
During a session
- The structure of the topic made explicit: definitions, the key identity, and why the method works.
- You work the next problem with guidance; mistakes are diagnosed, not just corrected.
- A check of the result by substitution, a special case, or a second method.
After each session
- A short written summary of what was covered and what to watch for.
- A few practice problems matched to the gap that was found.
- Links to the relevant RIDA MATH explainer, learning path, or lab.
Sessions support learning. Graded work and exams always remain the student's own.
Consultation and professional services
For research, engineering, and teaching work.
Every engagement is scoped in writing first: what is included, what is not, and what you receive.
- 02Mathematical ConsultationA structured discussion of a model, a method, or an analytical approach — with a written summary of the options.Engineers and technical teams working with differential equations, transforms, or matrix formulations
- 03Research DiscussionCareful mathematical conversation about your direction, notation, and arguments — so you can continue your own work.Graduate students and independent researchers
- 04Problem-Solving SessionsA focused session on one hard problem or method, where the goal is a route you understand — not an answer handed over.Students stuck on a method across several problems
- 05Workshops & LecturesConcept-led sessions for classes, student groups, and institutions — built around visual structure and purposeful exercises.University departments and student societies
- 06Educational Content DevelopmentAccurate, readable mathematical notes, lessons, exercises, and diagrams for a defined audience.Educators and course designers
Learning pathways and resources
Seven pathways, from foundations to research reading.
Each pathway lists prerequisites, outcomes, and ordered modules, and connects to explainers, labs, and the book where it genuinely applies.
- 01University FoundationsThe algebra, functions, trigonometry and exponential reasoning that university calculus assumes from the first lecture. It ends with an informal but careful introduction to limits, so the first formal course starts on solid ground.
- 02University CalculusSingle-variable and multivariable calculus as taught across Calculus I–III: limits, derivatives, integrals, series, partial derivatives and multiple integrals. The emphasis is on knowing why each technique applies, not only how to run it.
- 03Differential EquationsOrdinary differential equations from first-order equations through linear constant-coefficient equations, systems and Laplace transform methods, ending with initial and boundary value problems. Every method is paired with a way to check its answer.
- 04Transform MethodsThe Laplace, Fourier and Mellin transforms, their operational rules and convolution, studied both as computational tools and as related constructions. The final module connects this classical material to the operator-based framework of chapters 2 and 3 of the book.
- 05Linear Algebra and MatricesVector spaces, linear maps, matrices and eigen-structure, including spaces of functions and the matrix of differentiation. The path ends with the Matrix Boundary Method described in chapter 5 of the book.
- 06Complex Variables and Root GeometryComplex numbers, polar form, roots of polynomials and rational functions, with attention to where roots lie and what that location implies. The later modules connect this to the angular–hyperbolic representation in chapter 3 of the book and the trigonometric and hyperbolic root representation in chapter 4.
- 07Research ReadingHow to read mathematical research and technical books, including the RIDA MATH book itself: notation, definitions, claims and the status of each statement. The path is practiced on real text, with a written reading note as the product of each unit.
Community
A moderated place for careful mathematics.
Eight topic channels, curated problems, study circles, and reading sessions. Every contribution is reviewed before it appears, and current graded work is never discussed.
Where do the zeros of a derivative sit?
For , find the real zeros of . Express them as and explain the pattern.
Open in channelMath Lab
Five instruments for seeing structure.
Change a parameter and watch the mathematics respond. Each lab states its supported domain and the difference between demonstration and proof.
- Lab 01Derivative LabWhat does the n-th derivative look like without repeated expansion?
- Lab 02Transform LabHow do a kernel and a region of convergence turn a function into its transform?
- Lab 03Angular–Hyperbolic LabWhy do bounded kernels give angles and unbounded kernels give hyperbolic angles?
- Lab 04Root Geometry LabHow does the position of the roots control a rational function's derivatives?
- Lab 05Matrix Boundary LabCan an integral be evaluated by solving one small linear system instead of integrating by parts?
Research
Five analytical worlds, classified honestly.
Each area separates classical foundations from the frameworks and formulations proposed in Rida's book.
01Higher-Order Parametric Derivatives via Definite IntegralsEvaluating high-order parametric derivatives as single definite integrals, without repeated quotient rules.
02An Operator-Based Framework for Integral TransformsLaplace, Fourier, and Mellin transforms generated from one kernel by repeated differentiation.
03Mathematical Geometry: Angular–Hyperbolic RepresentationReading Laplace transforms through circular and hyperbolic coordinates in the damping–frequency plane.
04Root Geometry and Higher Derivatives of Rational FunctionsClosed formulas for derivatives of rational functions, read from the geometry of roots.
05Matrix Boundary MethodTruncated Laplace integrals and linear ODEs reduced to one resolvent linear system.
Every statement on RIDA MATH carries one of seven labels, for example
- Classical Foundation
- Book Framework
- Proposed Formulation
- Computational Demonstration
- Complexity
- Structure
- Geometry
- Unification
- Computation
- Understanding
Journal
Explainers and practical guides.
Long-form pieces with equations, worked examples, references, and links into the labs and pathways.
- The Structure Behind Higher-Order DerivativesWhy the -th derivative of a quotient such as becomes unmanageable by the quotient rule, and how moving the parameter inside a definite integral turns it into one readable formula.
- A Geometric View of Laplace Transform BehaviorSeparating damping from frequency places every oscillatory Laplace transform at a point of the -plane, where a radius controls decay and an angle controls sign and shape.
- How to Read a Mathematical DefinitionA practical method for reading definitions: parse the quantifiers, separate standing conditions from the claim, build examples and non-examples, probe edge cases, and write the negation. Worked on the ε–δ limit and on linear independence.
Publication · First edition, August 2026
Unified Analytical Methodsfor Higher-Order Derivatives, Integral Transforms, and Matrix-Based Techniques
Rida's first book connects higher-order derivatives, an operator view of integral transforms, angular–hyperbolic geometry, root geometry, and the Matrix Boundary Method — for advanced undergraduates, graduate researchers, and engineers.
About
Rida Jamal Badawi Abu-Sokon
A mathematics teacher and independent Jordanian researcher with a bachelor's degree from Al-Zaytoonah University of Jordan. His research interests are integral transforms and differential operators, with an emphasis on analytical methods for higher-order derivatives and matrix-based techniques.
- ORCID
- 0009-0008-3182-5300
- Contact
- Rida.313.jamal@gmail.com
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